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Question 2
Prove that: sec2 θ+cosec2 θ=tan θ+cot θ

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Solution

LHS=sec2 θ+cosec2 θ

=1cos2 θ+1sin2 θ[sec θ=1cos θ and cosec θ=1sin θ]

=sin2 θ+cos2 θsin2 θ.cos2 θ=1sin2 θ.cos2 θ [sin2 θ+cos2 θ=1]

=sin2 θ+cos2 θsin2 θ.cos2 θ=1sin2 θ.cos2 θ [1=sin2 θ+cos2 θ]

=sin2 θsin θ.cos θ+cos2 θsin θ.cos θ

=sin θcos θ+cos θsin θ [tan θ=sin θcos θ and cot θ=cos θsin θ]

=tan θ+cot θ=RHS


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